A note on the compartmental analysis and related issues in laser Doppler flowmetry

Compartmental analysis (CA) in laser Doppler flowmetry (LDF) means deciphering the nutritional and thermoregulating flows from the measured perfusion flux. Based on the new theories proposed in J. Zhong and G. Nilsson (ibid., vol. 40, 1993) and J. Zhong et al. (ibid., vol. 45, p. 354-64, 1998), the CA is formulated here as an optimal approximation without directly involving the geometric information of the vessel network. It is seen that this approximation approach could also solve the biological zero (BZ) problem simultaneously, therefore, it actually provides a systematic solution to the BZ problem without estimating the BZ flux experimentally. In addition, the BZ problem with compartmental differences is reformulated, and the condition under which multiple compartments can be treated as a single one is investigated. The result, together with some computer simulations, showed that the theory in J. Zhong et al. is still an easy and useful approximation in practice. This note serves as a useful supplement to J. Zhong and G. Nilsson and J. Zhong et al. and may help to solve and clarify some critical problems in LDF.